Using a fork, pierce the skin of each tomato several times. Place cut side down on a paper towel and let drain for 30 minutes.
In a large skillet, heat 1 tablespoon olive oil over medium-low heat. Add the drained tomatoes, cut side up, and cook uncovered until tender, 30 minutes to 1 hour, depending on ripeness.
Preheat the broiler. In a small bowl, combine 2 teaspoons olive oil with the garlic, basil, sage, parsley, thyme, salt and pepper. Brush a baking sheet with the remaining olive oil; place the tomatoes, cut side up, on the sheet. Divide the herb mixture evenly among the tomato halves, pressing in well, then drizzle with any liquid from the skillet. Broil until browned, 2 to 3 minutes. Serve hot or at room temperature.